The impulse response of a data channel such as a communications or magnetic recording channel is important for determining parameters of various media and signal processing components. In magnetic recording, where non-return to zero (NRZ) modulation format is usually adopted, the impulse response of the recording channel corresponds essentially to the pulse, or “dibit”, response, i.e. the response of the channel to a pulse input. The step, or “transition”, response of the recording channel, i.e. the response of the channel to a step input, can be derived from this dibit response. The dibit and transition responses of the magnetic recording channel in data storage devices such as hard-disk drives and tape drive systems are very important for the design of the detection circuitry as well as for characterization of media, head, and read-channel components generally. One of the most important applications of the response identification is the off-line computation of the equalizer coefficients. This procedure is normally performed during manufacture of the storage device. Known techniques involve the recording of a pseudo-random binary sequence (PRBS), and the capture and processing of the T-spaced sampled or oversampled readback waveform, where 1/T is the symbol rate of the input PRBS. After collection of an appropriate number of readback samples, computation of the equalizer coefficients is usually performed either by a dedicated hardware engine or by software executed in a microcontroller. An example of this is described in US Patent Application Publication No. US 2003/0028833 A1. The set of equalizer coefficients can then be used during normal operation of the storage device, either as they stand or as an initial set of coefficients that can be updated by an adaptive procedure during operation.
Another important application of the dibit and transition responses is the characterization of nonlinear write effects which cause significant degradation at high linear recording densities. Nonlinear distortion cannot, in general, be corrected by equalization. It is therefore particularly important that these effects are correctly identified and quantified. Known techniques for identifying these effects again involve the recording of PRBS sequences and identification of the dibit response. An example is described in “Identification of Nonlinear Write Effects using Pseudorandom Sequences”, Palmer et al, IEEE Transactions on Magnetics, Vol. MAG-23, No. 5, September 1987.
In hard-disk drives, the recording data rate 1/T is very high, and usually the sampling interval of the readback signal is equal to the inverse of this data rate, i.e. T. As a consequence the use of PRBSs leads to a very simple multiplication-free correlation method for extracting the dibit response of the magnetic recording channel. Such schemes lend themselves to very simple hardware implementations. For oversampled waveforms, i.e. where the channel output signal is sampled at a higher rate than 1/T, such a simple approach is not feasible. For example, tape drives use oversampled waveforms with a typical value of 5/4 for the oversampling factor. In general, if the sampling interval for the channel output is permitted to take values TS=(q/p)T, where p and q are relative prime integers with q<p, the oversampled channel response may be extracted by first identifying each of the p subchannels of the overall dibit channel response, and then overlaying the resulting subchannel responses, see “Least-squares Storage Channel Identification”, J. M. Cioffi, IBM J. Res. Develop., Vol. 30, No. 3, May 1986. Unfortunately, this method requires multiplication of real numbers, rendering its implementation in hardware or software impractical.
While the foregoing has focussed primarily on magnetic recording systems, similar considerations apply in other systems, particularly data communications systems. It will therefore be apparent that a computationally efficient procedure for identifying the impulse response of a data channel would be highly desirable.